Australian AMC 2012 - Senior Question 24

Question 24

A spherical ball of radius 1 rests inside a holder in the shape of an inverted pyramid. The pyramid has a horizontal square top and its other faces are equilateral triangles. It is large enough to enclose the ball.

Question illustration

How far is the centre of the ball above the apex X of the pyramid?

$\sqrt2$
$\frac32$
$3-\sqrt2$
$\sqrt3$
2